Physics of Skydiving

Physics of Skydiving

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The Forces at Work

... God OBVIOUSLY intended for us to skydive. After all He DID create gravity!

So exactly what forces are acting on the skydiver? Well, of course there's the obvious one, the force of gravity of the Earth. This force is exerted on everything on the Earth and is exerted on the skydiver even though there is no direct contact between the skydiver and the Earth. This type of force, when two objects exert forces on one another even though they are not touching, is known as a noncontact force.

According to Newton's second law, the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object; or

Fnet =ma

The gravitational force that the Earth exerts on the skydiver is equal to the weight of the object on Earth. The acceleration of the gravitational force is the acceleration due to gravity (g), which is the acceleration of an object under the sole influence of gravity. Thus, the weight of an object is a product of its mass and acceleration due to gravity or


The acceleration due to gravity (g) near the Earth's surface is a constant that was determined to be 9.80 m/s. So, the weight of an object depends on how much mass an object has. The mass of an object is a quantitative measure of inertia, where inertia is the natural tendency of an object to stay at rest or in motion at a constant speed along a straight line.

Air Resistance

Another force acting on the parachutist is air resistance. Air resistance is the colliding of an object with molecules of air. The falling skydiver collides with air molecules during the downward fall. These air molecules create a force pushing upward which is opposite to the skydiver's direction, as well as the force of gravity. Air Resistance is more complicated force than the force of gravity because it is a nonconservative force. A nonconservative force is one in which the work it does on an object moving in between two points depends on the path of the motion between the two points.

The amount of air resistance encountered by the skydiver depends mainly on two factors:

1: The speed of the skydiver.

2: The cross-sectional area of the skydiver.

An increase in the speed and/or the amount of cross-sectional area leads to an increase in the amount of air resistance encountered.

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I'll go into more detail as I delve into the next topic--terminal velocity.

Terminal Velocity

The speed of a skydiver increases every second as he or she plummets towards the ground. This increase in speed results in an increase in the amount of air resistance. The speed and the amount of air resistance increase until the amount of air resistance is large enough to counter the force of gravity. When this happens, the forces of air resistance and gravity balance themselves out, the net force will be equal to 0 Newtons, and the skydiver stops accelerating. At this point the skydiver reaches what is called the terminal velocity. The constant terminal velocity is the greatest speed that the skydiver will reach on his way down.

Another factor in the terminal velocity of the skydiver is the cross-sectional area. A skydiver who has his arms and legs spread out (usually referred to as the arch position),

will meet with more air resistance than one who fall straight down head down.

The greater air resistance encountered by the greater cross-sectional area of the arch position, results in the achievement of terminal velocity more quickly than that of the tuck position. The terminal velocity of the arch position will also be slower than that of the tuck position.

The skydiver will continue to fall at this constant speed (terminal velocity) unless something happens to the change the speed of the skydiver or the amount of airresistance encountered--something like a parachute.

How a Parachute Works.

So, how does a parachute slow your descent, allowing you to float safely to the ground instead of ramming into it? The answer is simple considering what I just told you about air resistance. When the parachute is fully opened, the cross-sectional area of the skydiver is increased and thus the amount of air resistance encountered by the skydiver is increased. When the parachute is opened the force of air resistance becomes greater than the force of gravity. The net force on the descending skydiver now has an acceleration that points upward. This acceleration which is points in the opposite direction of the downward descent, causes a decrease in the skydiver's velocity. As the speed of descent decreases, the amount of air resistance also drops, until one again a terminal velocity is reached. This terminal velocity is now slow enough so that the skydiver can land safely on terra firma without his legs snapping in two. (That is of course, if the skydiver lands correctly.)

Summary and Conclusion

Here is a brief summary of what happens during a hypothetical skydive.

1) 100kg Guy jumps out of plane 2) Fgrav = 1000N down, Fair = 400N up Velocity increases, acceleration points downward.

3) Eventually Fgrav = Fair = 1000N

Terminal velocity achieved.

4) Parachute deployed. Fgrav = 1000N, Fair = 1600N

Velocity decreases, acceleration points upward

5) Eventually Fgrav = Fair = 1000N, again. Terminal velocity achieved again.

6) Skydiver floats safely to the ground

Skydiving Equipment


When I deploy my chute at the terminal velocity, my speed decreases from 50 to 5 m/s.

If it opens in small dT (time delta), than force would be enough to break my neck.

F=J/dT , where F-force, J-impulse(difference in momentum) , and dT - time required for canopy to open. Let's imagine that time is dT=1/2 sec and mass = 100kg.

Impulse will be dP=mv(final)-mv(initial) = (100kg)(5m/s)-(100kg)(50m/s) = -4500 kg*m/s

Force will be F=J/dT = (-4500 kg*m/s)/(1/2s) = -9000 N

This force is big enough to kill you.

Today's canopies have a mechanism that allows them to inflate gradually and slow enough, so that the openings feel more like standing up from a chair than collision with a heavy truck moving at 60mph... It is called "slider". It is just a piece of material, that has four holes for canopie's lines. When I pack my main, I move it all the way up to the material.

In this photo you can see slider right above the jumper.

While deploying, slider is still all the way up, which does not allow the canopy to inflate all the way. It takes several seconds for slider to move down.

Usually, I have a full inflated canopy after about 9 seconds. So, the force that is acting on me is

F=J/dT = (-4500 kg*m/s)/(9sec) = -500 N. This is very much survivable :))

While freefalling there are two types of drag : induced and parasitic. Induced drag is the one that is created by skydiver's area. Parasitic drag is one that is created by skydiver's rough surface. The latter one prevents us from doing quick and exact motions. So, it is very helpful to reduce this drag.

Today's equipment has excellent aerodynamics. Jumpsuits are tight and homogeneous. Containers are thin and small, so they do not create any additional area.

Pilot Chute Hesitation

How do skydivers deploy their main canopies ? The first thing that comes on non-jumper's mind is "pulling a ring". Even though it is true for student and reserve parachutes, regular skydivers use enother method. Pilot chute is simply stowed in the bottom of the container. It is completely hidden inside with an exception of one little handle sticking out.

When it's time to deploy, you simply grab the handle, pull the pilot chute out, and throw it to the air. Pilot chute is connected to the bridle, which is linked to the canopy on its other side(actually, to the bag which has the parachute in it, to be excact).

Some calculations :

A pilot chute with radius R=34 cm at the terminal speed will have a drag

d=(1/2))CpAv^2, where C- drag coefficient (varies from 0.4 to 1.0), p- density of the air(1 kg/m^3), v is velocity, and A is effective cross-section.

d= (1/2)(.8)(1kg/m^3)(.34m)^2(3.14)(50m/s)^2 = 363 N

But here is the potential problem. A skydiver falling at a big speed necessary has an area of low pressure behind his back. Density of the air in that area is significally lower, which does not provide enough drag force in order to lift the parachute.

Two things can be done to prevent this malfunction. When you pull the pilot chute out, do not just let it go, but throw it to the side, where there is enough air. If hesitation happened, turn to your side, and the air pressure would increase.
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